A Self-consistent, Unified Approach to the Reflection and Acceleration of
Pickup Ions at the Solar Wind Termination shock and Upstream Modulation of
Anomalous Cosmic Rays.
J.A. le Roux, G.P. Zank
Bartol Research Institute, University of Delaware,
Newark, Delaware, USA
H. Fichtner
Institute for Theoretical Physics, Ruhr-University
Bochum, Bochum, Germany
The current theoretical framework of non-linear diffusive shock acceleration
traditionally used to model the formation of anomalous cosmic rays (ACRs) at
the termination shock and its affect on the shock structure and position is
ill suited for this purpose. The theory, based on the assumption of isotropic
or near-isotropic particle distributions, does not deal with the highly
anisotropic nature of pickup ion (PUI) reflection and initial acceleration at
the shock before diffusive shock acceleration dominates. To address this
problem, we adopt a time-dependent HD approach in which a one fluid description
of the solar wind with PUI protons, under the dynamic influence of multiply
reflected ion (MRI) accelerated PUI protons as the second and ACR protons as
the third fluid, is followed. In the process we make use of the semi-analytical
theory of MRI acceleration as presented by Zank et al. [1996] to specify
appropriate loss terms that describe self-consistently the effect of MRI
acceleration on the termination shock structure and position. To close the set
of HD equations, the ACR transport equation is solved with a self-consistently
determined source of PUI protons based on a combination of PUI transport theory
and MRI theory. The ACR radial diffusion coefficient is simulated theoretically
on the basis of ACR diffusion tensor theory and a recent MHD transport model
for solar wind turbulence. The results show the following: (i) Both MRI
accelerated PUI protons and ACR protons might have a significant affect on the
position and macrostructure of the termination shock. (ii) The modeled ACR
spectrum at the shock has complex features reflecting the non-linearity of the
diffusive acceleration process, for example. (iii) This unified approach yields
reasonable upstream ACR modulated spectra in the light of Voyager observations.